I'm not a pro either, but the way I do stems is, when I'm cutting out the pattern, on the inside curve instead of cutting 1/4" away from my stitching line, I just cut a lot of excess, like a straight line from the top to the bottom of the stem. I cut the outside curve scant 1/4" away, and then I pin it all down on the background fabric. That way, it's a whole big piece rather than a floppy stem. I then stitch the outside curve first, and when I get to the inside curve, I only cut maybe 2 to 3 inches at a time, at the scant 1/4" from the stitch line, and after that's been stitched, I move on to the next 2 to 3".
I hope that makes sense. Bottom line is, you're working with a bigger, sturdier piece while you're stitching your first side of the stem, allowing it to lay flat and not move around like a flimsy floppy stem.